Computer-Implemented Systems And Methods For Implementing Dynamic Trading Strategies In Risk Computations

ABSTRACT

Systems and methods are provided for simulating a portfolio risk of a portfolio managed according to one or more portfolio management rules. An initial holding amount of an investment instrument is received, and a portfolio management rule is received. One or more risk factors are simulated a first time period into the future. An adjustment amount is determined based on the portfolio management rule and the one or more risk factors simulated a first time period into the future and the holding amount of the investment instrument is adjusted based on adjustment amount. The one or more risk factors are simulated a second time period into the future, and a portfolio risk value is calculated based on the adjusted holding amount and the one or more risk factors simulated a second time period into the future.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.61/326,890, filed Apr. 22, 2010, entitled “Computer-Implemented Systemsand Methods for Implementing Dynamic Trading Strategies in RiskComputations.” The entirety of which is herein incorporated byreference.

FIELD

The technology described herein relates generally to portfoliomanagement and more specifically to risk calculation in portfoliomanagement.

BACKGROUND

In conducting portfolio management, it is often desirable to identifythe risk involved with certain investments to help determine theattractiveness of an investment instrument or combination of investmentinstruments. For example, one may desire to identify a value at riskassociated with an investment portfolio. A value at risk measure (VaR)summarizes the worst loss over a target horizon with a given level ofconfidence. FIG. 1 depicts a distribution of 400 projected returns on aportfolio. Based on the distribution of FIG. 1, the worst expectedportfolio return with 95% confidence is −3.5%. With a portfolio valuedat $100M, the worst expected portfolio return results in a value at riskmeasure of $3.5M.

SUMMARY

Systems and methods are provided for simulating a portfolio risk of aportfolio managed according to one or more portfolio management rules.An initial holding amount of an investment instrument may be received,and a portfolio management rule may be received. One or more riskfactors may be simulated a first time period into the future. Anadjustment amount is determined based on the portfolio management ruleand the one or more risk factors simulated a first time period into thefuture and the holding amount of the investment instrument may beadjusted based on the adjustment amount. The one or more risk factorsmay be simulated a second time period into the future, and a portfoliorisk value may be calculated based on the adjusted holding amount andthe one or more risk factors simulated a second time period into thefuture.

As another example, a system may include a data processor and acomputer-readable memory, where the computer-readable memory includesinstructions for commanding the data processor to perform a method. Inthe method, an initial holding amount of an investment instrument may bereceived, and a portfolio management rule may be received. One or morerisk factors may be simulated a first time period into the future. Anadjustment amount is determined based on the portfolio management ruleand the one or more risk factors simulated a first time period into thefuture and the holding amount of the investment instrument may beadjusted based on the adjustment amount. The one or more risk factorsmay be simulated a second time period into the future, and a portfoliorisk value may be calculated based on the adjusted holding amount andthe one or more risk factors simulated a second time period into thefuture.

As a further example, a computer-readable memory may be encoded withininstructions for commanding a data processor to perform a method. In themethod, an initial holding amount of an investment instrument may bereceived, and a portfolio management rule may be received. One or morerisk factors may be simulated a first time period into the future. Anadjustment amount is determined based on the portfolio management ruleand the one or more risk factors simulated a first time period into thefuture and the holding amount of the investment instrument may beadjusted based on the adjustment amount. The one or more risk factorsmay be simulated a second time period into the future, and a portfoliorisk value may be calculated based on the adjusted holding amount andthe one or more risk factors simulated a second time period into thefuture.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a distribution of projected returns on a portfolio.

FIG. 2 depicts a computer-implemented environment for simulating aportfolio risk of a portfolio managed according to one or more portfoliomanagement rules.

FIG. 3 is a flow diagram depicting a process for calculating a value atrisk using a Monte Carlo simulation.

FIG. 4 is a diagram depicting the results of a Monte Carlo simulationfor a value at risk calculation.

FIG. 5 is a flow diagram depicting a process for calculating a value atrisk using a Monte Carlo simulation that incorporates dynamic portfoliomanagement.

FIGS. 6 and 7 are tables describing an example Monte Carlo simulation ofportfolio risk of a portfolio managed according to one or more portfoliomanagement rules.

FIG. 8 is a flow diagram depicting a computer-implemented method forsimulating a portfolio risk of a portfolio managed according to one ormore portfolio management rules.

FIGS. 9A, 9B, and 9C depict example systems for a portfolio risk.

DETAILED DESCRIPTION

FIG. 2 depicts at 100 a computer-implemented environment for simulatinga portfolio risk of a portfolio managed according to one or moreportfolio management rules. A user 102 interacts with a portfoliosimulator 104 to determine how much risk is involved with a portfoliomanaged according to a strategy represented by one or more portfoliomanagement rules 114.

In traditional risk management, portfolios are assumed static (e.g.,they do not change over time and market states). While this assumptionmay be appropriate for market risk management over a short time horizon,such an approach may be undesirable in other contexts where longer timehorizons are the focus. Thus, a portfolio simulator 104 may enable arisk management system that better accommodates the dynamic nature of aportfolio.

Dynamic trading strategies allow one to track risk over time, ratherthan using a static framework with a single time step or a model forextrapolating risk. Trading strategies can be modeled throughevent-based rules. For example, arbitrary rules may be applied that takeany information from a scenario and use that information to adjust theportfolio, resulting in a portfolio whose composition is bothtime-dependent and scenario-dependent to more accurately represent anactively managed portfolio. Stop-loss orders, delta hedging, durationmatching, and other strategies may be represented by one or moreportfolio management rules that can be simulated by a portfoliosimulator. The introduction of dynamic trading strategies enables toolsof risk management, such as Monte Carlo simulation, historicalsimulation, covariance simulation, scenario simulation, and stresstesting to be applied to asset/liability and credit managementsituations. Such valuation models that account for portfolio effects cansignificantly improve the accuracy of calculations. A dynamic portfoliomay be modeled utilizing one or more portfolio management rules. Suchrules may be easy to communicate and can capture the nature of a firm'sbehavior, while being robust under uncertainty.

The users 102 can interact with the portfolio simulator 104 through anumber of ways, such as over one or more networks 108. Server(s) 106accessible through the network(s) 108 can host the portfolio simulator104. One or more data stores 110 can store the data to be analyzed bythe portfolio simulator 104 as well as any intermediate or final datagenerated by the portfolio simulator 104. The one or more data stores110 may contain many different types of data associated with theprocess, including risk factor data 112, portfolio management rules 114,as well as other data. The portfolio simulator 104 can be an integratedweb-based reporting and analysis tool that provides users flexibilityand functionality for simulating a portfolio risk. It should beunderstood that the portfolio simulator 104 could also be provided on astand-alone computer for access by a user 102.

A portfolio may include financial instruments, such as stocks, options,and futures; credit instruments, such as loans, bonds, and options;commodities, such as gas, pork bellies, and wheat; and currencies, suchas the Japanese Yen, the U.S. Dollar, and the British Pound. The valueof a portfolio may be calculated according to the following formula:

${{Val} = {\sum\limits_{i = 1}^{N}{h_{i}{p_{i}\left( {{rf}_{1},{rf}_{2},\ldots \mspace{14mu},{rf}_{R}} \right)}}}},$

where N is the number of instruments in the portfolio, R is the numberof risk factors, rf_(j) is the value of risk factor j, h_(i) is thenumber of holdings of instrument i, and p_(i)(rf₁, rf₂, . . . , rf_(R))represents the value (price) of instrument i, as a function of riskfactors 1 . . . R.

FIG. 3 is a flow diagram depicting a process for calculating a value atrisk using a Monte Carlo simulation. At 302, the system is initializedto include the time horizon for the simulation (T), the size of the timestep to be taken at each generation t, where t<T, and the number ofdraws to be taken at each time step, n. The system is primed with a basecase at 304. For example, the base case may include starting values forall of the risk factors, instruments, holdings, and initial portfoliovalue. A time step is taken at 306, where, at 308, each risk factor isperturbed n times from the base case, giving n simulated market statesat a first time period in the future, whererf_(j,d,1)=rf_(j,0,0)+ε_(j,d,1), where rf_(j,d,t) is the value of riskfactor j along draw path d in {1, 2, . . . , n} at time t, ε_(j,d,t) isa random adjustment computed from a random draw, and rf_(j,0,0) is thebase case value for risk factor j. At 310, for each of the simulatedmarket states d in {1, 2, . . . , n}, the portfolio is priced, and thereturn on the portfolio is calculated relative to the base case,assuming a constant holding h_(i) for the time period between t=0 andt=1. A return distribution may be calculated at 312, such as is shownabove with respect to FIG. 1, and a value at risk may be calculated attime step 1 at 314 by picking a confidence level α, finding the worstreturn at that confidence level, and multiplying that return by thevalue of the base case portfolio. At 316, for each step {2 . . . T},steps 306, 308, 310, 312, and 314 may be repeated where draws made at308 follow a path: rf_(j,d,t)=rf_(j,d,(t−1))+ε_(j,d,t).

FIG. 4 is a diagram depicting the results of a Monte Carlo simulationfor a value at risk calculation. At each step 402, 404, 406 in thesimulation, a corresponding value at risk 410, 412, 414 is calculatedrelative to the base case 416. For example, the value at risk may becalculated by generating a distribution at each step 402, 404, 406 ofportfolio values calculated based on risk factor values of each draw418, 420, 422 at that step. The generated distribution at a step maythen be analyzed to determine a worst case return scenario with acertain degree of confidence, such as 95%. That worst case return at thedesired confidence may be applied to the base portfolio value tocalculate the value at risk.

The value of the examples described above may be somewhat limited inthat the holdings of the portfolios are assumed to be constant at eachstep. This assumption may not be realistic for longer time horizons(e.g., greater than 2 days), where adjustments to the portfolio may bemade, such as is the case in credit risk and asset liability management.FIG. 5 is a flow diagram depicting a process for calculating a value atrisk using a Monte Carlo simulation that incorporates dynamic portfoliomanagement.

At 502, the system is initialized to include the time horizon for thesimulation (T), the size of the time step to be taken at each generationt, where t≦T, and the number of draws to be taken at each time step, n.The system is primed with a base case at 504. For example, the base casemay include starting values for all of the risk factors, instruments,holdings, and initial portfolio value. A time step is taken at 506,where, at 508, each risk factor is perturbed n times from the base case,giving n simulated market states at a first time period in the future,where rf_(j,d,1)=rf_(j,0,0)+ε_(j,d,1), where rf_(j,d,t) is the value ofrisk factor j along draw path d in {1, 2, . . . , n} at time t,ε_(j,d,t) is a random adjustment computed from a random draw, andrf_(j,0,0) is the base case value for risk factor j.

At 510, for each of the simulated market states d in {1, 2, . . . , n},the portfolio is priced. At 512, trading strategies may be run. Forexample, trading strategies may be represented by one or more portfoliomanagement rules that are evaluated at 512. A collection of one or moreportfolio management decision rules can be used to represent a user's(firm's) behavior. Implementations of rules can leverage a broad rangeof technologies, such as from the field of artificial intelligence. Adecision rule may take the form of if ( . . . ) then ( . . . ). Thedecision rule has a left side and a right side. The left side is matchedagainst what is true in the world (facts) or what is believed to be true(beliefs). The right hand side describes what actions should be takengiven the left hand side is, or is believed to be, true. Facts can berepresented using predicate logic, first-order logic, or higher orderlogics. Beliefs may be represented by belief networks, neural networks,or any reasoning technology such as probabilistic or deterministic.Actions may be many things, such as asserting new facts about the world,updating databases, updating beliefs, computing results.

Decision rules can be grouped to form portfolio management tradingstrategies. The rules within a trading strategy can execute within anexpert system. Expert systems are very good for modeling expertbehavior. An expert system may allow rules to run in parallel, representknowledge through higher order logics, reach inferences through forwardchaining, and construct facts through backward chaining. Expert systemsmay also simplify the construction of robust rules and allow forefficient execution of forward chaining, such as via the CLIPS system.The use of forward chaining may capture non-linear relationships betweenrules.

With reference back to FIG. 5, running trading strategies at 512 mayinclude evaluating one or more portfolio management rules based on theone or more risk factors simulated a first time period into the futureat 508. The trading strategy execution at 512 may further includeadjusting the holding amount h_(i,d,t) for instrument i along draw pathd at time step t based on the evaluation of the one or more portfoliomanagement rules. A return distribution may be calculated at 514 and avalue at risk may be calculated at time step 1 at 516 by picking aconfidence level α, finding the worst return at that confidence level,and multiplying that return by the value of the base case portfolio. At518, for each step {2 . . . T}, steps 506, 508, 510, 512, 514 and 516may be repeated where draws made at 508 follow a path:rf_(j,d,t)=rf_(j,d(t−1))+ε_(j,d,t).

FIGS. 6 and 7 are tables describing an example Monte Carlo simulation ofportfolio risk of a portfolio managed according to one or more portfoliomanagement rules. In this example, two instruments are utilized, eachwith an initial holding of 10. The simulation is performed over two timesteps with ten random draw paths taken over those two steps. The exampleseeks to calculate a value at risk with a 90% confidence based on threefactors. It is assumed that a limitless amount of cash is available tobuy and sell shares. The initial state for the example is as follows:

Holding 1: h_(1,0,0)=10;

Holding 2: h_(2,0,0)=10;

Price of holding 1: p₁(rf₁, rf₂, rf₃)=rf₁+10;

Price of holding 2: p₂(rf₁, rf₂, rf₃)=rf₂+rf₃;

Time steps: s=2;

Draws: d=10.

The risk factors and prices of the holdings at t=0 are:

rf_(1,0,0)=4

rf_(2,0,0)=2

rf_(3,0,0)=7

p₁(rf_(1,0,0),rf_(2,0,0),rf_(3,0,0))=14

p₂(rf_(1,0,0),rf_(2,0,0),rf_(3,0,0))=11,

which results in an initial portfolio value of (14*10)+(9*10)=230. Thefollowing portfolio management rules are to be applied as a tradingstrategy for the simulation:

1. if p₂(rf_(1,d,s),rf_(2,d,s),rf_(3,d,s))≦5 thenh_(2,d,s)=½h_(2,d,(s−1)) and h_(1,d,s)=h_(1,d,(s−1))+2; and

2. if h_(1,d,s)−h_(2,d,s)≧10 then h_(2,d,s)=h_(2,d,(s−1))+1 andh_(1,d,s)=h_(1,d,(s−1))−1.

Table 1, depicted in FIG. 6 illustrates ten sets of random draws, d={1 .. . 10}, for each of the three risk factors rf₁, rf₂, and rf₃. Table 2depicts an evaluation of the price of holding 1, p₁, and the price ofholding 2, p₂, at t=1 for each of the ten draws based on the drawn riskfactor variables. For example, evaluating p₁ and p₂ for draw d=1 basedon the drawn risk factor values rf_(1,1,1)=1, rf_(2,1,1)=3, andrf_(3,1,1)=2 calculates a price of holding 1 of p₁=11 and a price ofholding 2 of p₂=5. Table 3 depicts the state of the holdings for thefirst time period after the trading strategy is executed, as depicted at512 in FIG. 5. For example, based on the first portfolio managementrule, because the price of holding 2, p₂, is equal to 5 for draw d=1,then the number of instruments of holding 2, h_(2,1,1), is halved andthe number of instruments of holding 1, h_(1,1,1), is increased by 2.Table 4 depicts a calculation of the portfolio value and return for eachof the ten draws at time t=1 as compared to the initial portfolio valueof 230. As described above, the portfolio value may be calculatedaccording to:

${Val} = {\sum\limits_{i = 1}^{N}{h_{i}{{p_{i}\left( {{rf}_{1},{rf}_{2},\ldots \mspace{14mu},{rf}_{R}} \right)}.}}}$

The value at risk calculation for the first time step is calculatedbased on the confidence level of 90%. In this example, the worst returnat a 90% confidence interval is −31% at draw d=1, which corresponds witha value at risk of 73.

Table 5, depicted in FIG. 7, depicts a second set of ten draws from thet=1 values for the three risk factors. Table 6 depicts a calculation ofthe price of holding 1, p₁, and the price of holding 2, p₂, at t=2 foreach of the ten draws. Table 7 depicts an evaluation of the twoportfolio rules and the adjustment of the holdings based on thatevaluation. For example, for draw d=1, based on the first portfoliomanagement rule, because the price of holding 2 is equal to 5, theamount of holding 2, h_(2,1,2) is halved to three, and the amount ofholding 1, h_(1,1,2), is increased to 14. Based on the second portfoliomanagement rule, because the difference in the amount of holding 1 andthe amount of holding 2 is greater than ten, then the amount of holding1 is increased by 1 to 4, and the amount of holding 2 is decreased by 1to 13. Table 8 depicts a calculation of the portfolio value and returnat time t=2 as compared to the initial portfolio value of 230. The valueat risk may be computed for the second time based on the confidenceinterval of 90%. The worst return at a 90% confidence interval is −23%,which results in a value at risk of 54.

FIG. 8 is a flow diagram depicting a computer-implemented method forsimulating a portfolio risk of a portfolio managed according to one ormore portfolio management rules. An initial holding amount of one ormore investment instruments is received at 802. At 804, one or moreportfolio management rules are received, and at 806, one or more riskfactors are simulated a first time period into the future. At 808, theone or more portfolio management rules are evaluated based on the one ormore risk factors simulated a first time period into the future, and theholding amounts of the one or more investment instruments are adjustedbased on the evaluation of the portfolio management rules. At 810, theone or more risk factors are simulated a second time period into thefuture, and at 812, a portfolio risk value is calculated based on theadjusted holding amounts and the one or more risk factors simulated asecond time period into the future. For example, the portfolio riskvalue may be a value at risk, an expected return, a portfolio valuevariance, a portfolio value standard deviation, an expected returnconfidence interval, an expected portfolio value, as well as others.

FIGS. 9A, 9B, and 9C depict example systems for simulating a portfoliorisk of a portfolio managed according to one or more portfoliomanagement rules. For example, FIG. 9A depicts an exemplary system 900that includes a stand alone computer architecture where a processingsystem 902 (e.g., one or more computer processors) includes a system forsimulating a portfolio risk 904 being executed on it. The processingsystem 902 has access to a computer-readable memory 906 in addition toone or more data stores 908. The one or more data stores 908 may containrisk factors 910 as well as portfolio management rules 912.

FIG. 9B depicts a system 920 that includes a client server architecture.One or more user PCs 922 access one or more servers 924 running a systemfor simulating a portfolio risk 926 on a processing system 927 via oneor more networks 928. The one or more servers 924 may access a computerreadable memory 930 as well as one or more data stores 932. The one ormore data stores 932 may contain risk factors 934 as well as portfoliomanagement rules 936.

FIG. 9C shows a block diagram of exemplary hardware for a stand alonecomputer architecture 950, such as the architecture depicted in FIG. 9A,that may be used to contain and/or implement the program instructions ofsystem embodiments of the present invention. A bus 952 may serve as theinformation highway interconnecting the other illustrated components ofthe hardware. A processing system 954 labeled CPU (central processingunit) (e.g., one or more computer processors), may perform calculationsand logic operations required to execute a program. A processor-readablestorage medium, such as read only memory (ROM) 956 and random accessmemory (RAM) 958, may be in communication with the processing system 954and may contain one or more programming instructions for simulating aportfolio risk of a portfolio managed according to one or more portfoliomanagement rules. Optionally, program instructions may be stored on acomputer readable storage medium such as a magnetic disk, optical disk,recordable memory device, flash memory, or other physical storagemedium. Computer instructions may also be communicated via acommunications signal, or a modulated carrier wave.

A disk controller 960 interfaces with one or more optional disk drivesto the system bus 952. These disk drives may be external or internalfloppy disk drives such as 962, external or internal CD-ROM, CD-R, CD-RWor DVD drives such as 964, or external or internal hard drives 966. Asindicated previously, these various disk drives and disk controllers areoptional devices.

Each of the element managers, real-time data buffer, conveyors, fileinput processor, database index shared access memory loader, referencedata buffer and data managers may include a software application storedin one or more of the disk drives connected to the disk controller 960,the ROM 956 and/or the RAM 958. Preferably, the processor 954 may accesseach component as required.

A display interface 968 may permit information from the bus 952 to bedisplayed on a display 970 in audio, graphic, or alphanumeric format.Communication with external devices may optionally occur using variouscommunication ports 972.

In addition to the standard computer-type components, the hardware mayalso include data input devices, such as a keyboard 973, or other inputdevice 974, such as a microphone, remote control, pointer, mouse and/orjoystick.

This written description uses examples to disclose the invention,including the best mode, and also to enable a person skilled in the artto make and use the invention. The patentable scope of the invention mayinclude other examples. For example, the systems and methods may includedata signals conveyed via networks (e.g., local area network, wide areanetwork, internet, combinations thereof, etc.), fiber optic medium,carrier waves, wireless networks, etc. for communication with one ormore data processing devices. The data signals can carry any or all ofthe data disclosed herein that is provided to or from a device.

Additionally, the methods and systems described herein may beimplemented on many different types of processing devices by programcode comprising program instructions that are executable by the deviceprocessing subsystem. The software program instructions may includesource code, object code, machine code, or any other stored data that isoperable to cause a processing system to perform the methods andoperations described herein. Other implementations may also be used,however, such as firmware or even appropriately designed hardwareconfigured to carry out the methods and systems described herein.

The systems' and methods' data (e.g., associations, mappings, datainput, data output, intermediate data results, final data results, etc.)may be stored and implemented in one or more different types ofcomputer-implemented data stores, such as different types of storagedevices and programming constructs (e.g., RAM, ROM, Flash memory, flatfiles, databases, programming data structures, programming variables,IF-THEN (or similar type) statement constructs, etc.). It is noted thatdata structures describe formats for use in organizing and storing datain databases, programs, memory, or other computer-readable media for useby a computer program.

The computer components, software modules, functions, data stores anddata structures described herein may be connected directly or indirectlyto each other in order to allow the flow of data needed for theiroperations. It is also noted that a module or processor includes but isnot limited to a unit of code that performs a software operation, andcan be implemented for example as a subroutine unit of code, or as asoftware function unit of code, or as an object (as in anobject-oriented paradigm), or as an applet, or in a computer scriptlanguage, or as another type of computer code. The software componentsand/or functionality may be located on a single computer or distributedacross multiple computers depending upon the situation at hand.

It may be understood that as used in the description herein andthroughout the claims that follow, the meaning of “a,” “an,” and “the”includes plural reference unless the context clearly dictates otherwise.Also, as used in the description herein and throughout the claims thatfollow, the meaning of “in” includes “in” and “on” unless the contextclearly dictates otherwise. Finally, as used in the description hereinand throughout the claims that follow, the meanings of “and” and “or”include both the conjunctive and disjunctive and may be usedinterchangeably unless the context expressly dictates otherwise; thephrase “exclusive or” may be used to indicate situation where only thedisjunctive meaning may apply.

1. A computer-implemented method for simulating a portfolio risk of aportfolio managed according to one or more portfolio management rules,comprising: receiving an initial holding amount of an investmentinstrument; receiving a portfolio management rule related to conditionsfor buying or selling the investment instrument; simulating one or morerisk factors that affect the value of the investment instrument a firsttime period into the future; determining an adjustment amount for theholding amount of the investment instrument based on the portfoliomanagement rule and the one or more risk factors simulated a first timeperiod into the future; adjusting the holding amount of the investmentinstrument based on the adjustment amount; simulating the one or morerisk factors a second time period into the future; and calculating aportfolio risk value based on the adjusted holding amount and the one ormore risk factors simulated a second time period into the future.
 2. Themethod of claim 1, further comprising determining a second adjustmentamount based on the portfolio management rule and the one or more riskfactors simulated a second time period into the future; and adjustingthe holding amount of the investment instrument based on the secondadjustment amount.
 3. The method of claim 2, further comprising:simulating the one or more risk factors a third time period into thefuture; and calculating a second portfolio risk value based on theadjusted holding amount and the one or more risk factors simulated athird time period into the future.
 4. The method of claim 1, furthercomprising: repeating the steps of simulating one or more risk factors afirst time period into the future, determining an adjustment amount,adjusting the holding amount, and simulating the one or more riskfactors a second time period into the future a plurality of times. 5.The method of claim 4, further comprising generating a distributionbased on the repeated steps; wherein the portfolio risk value iscalculated based on the distribution.
 6. The method of claim 5, whereinthe portfolio risk value is a value at risk (VaR) measure calculatedbased on the distribution.
 7. The method of claim 6, wherein the valueat risk (VaR) measure is calculated with a 95% confidence based on thedistribution.
 8. The method of claim 1, wherein simulating one or morerisk factors a first time period and simulating one or more risk factorsa second time period uses a Monte Carlo simulation method.
 9. The methodof claim 1, wherein the portfolio risk value is an expected return, aportfolio value variance, a portfolio value standard deviation, anexpected return confidence interval, an expected portfolio value, or arisk distortion measure.
 10. A computer-implemented system forsimulating a portfolio risk of a portfolio managed according to one ormore portfolio management rules, comprising: a data processor; acomputer-readable memory encoded with instructions for commanding a dataprocessor to perform steps comprising: receiving an initial holdingamount of an investment instrument; receiving a portfolio managementrule related to conditions for buying or selling the investmentinstrument; simulating one or more risk factors that affect the value ofthe investment instrument a first time period into the future;determining an adjustment amount for the holding amount of theinvestment instrument based on the portfolio management rule and the oneor more risk factors simulated a first time period into the future;adjusting the holding amount of the investment instrument based on theadjustment amount; simulating the one or more risk factors a second timeperiod into the future; and calculating a portfolio risk value based onthe adjusted holding amount and the one or more risk factors simulated asecond time period into the future.
 11. The system of claim 10, whereinthe steps further comprise determining a second adjustment amount basedon the portfolio management rule and the one or more risk factorssimulated a second time period into the future; and adjusting theholding amount of the investment instrument based on the secondadjustment amount.
 12. The system of claim 11, wherein the steps furthercomprise: simulating the one or more risk factors a third time periodinto the future; and calculating a second portfolio risk value based onthe adjusted holding amount and the one or more risk factors simulated athird time period into the future.
 13. The system of claim 10, whereinthe steps further comprise: repeating the steps of simulating one ormore risk factors a first time period into the future, determining anadjustment amount, adjusting the holding amount, and simulating the oneor more risk factors a second time period into the future a plurality oftimes.
 14. The system of claim 13, wherein the steps further comprisegenerating a distribution based on the repeated steps; wherein theportfolio risk value is calculated based on the distribution.
 15. Thesystem of claim 14, wherein the portfolio risk value is a value at risk(VaR) measure calculated based on the distribution.
 16. The system ofclaim 15, wherein the value at risk (VaR) measure is calculated with a95% confidence based on the distribution.
 17. The system of claim 10,wherein simulating one or more risk factors a first time period andsimulating one or more risk factors a second time period uses a MonteCarlo simulation method.
 18. The system of claim 10, wherein theportfolio risk value is an expected return, a portfolio value variance,a portfolio value standard deviation, an expected return confidenceinterval, an expected portfolio value, or a risk distortion measure. 19.A computer-readable memory encoded with instructions for commanding adata processor to perform steps comprising: receiving an initial holdingamount of an investment instrument; receiving a portfolio managementrule related to conditions for buying or selling the investmentinstrument; simulating one or more risk factors that affect the value ofthe investment instrument a first time period into the future;determining an adjustment amount for the holding amount of theinvestment instrument based on the portfolio management rule and the oneor more risk factors simulated a first time period into the future;adjusting the holding amount of the investment instrument based on theadjustment amount; simulating the one or more risk factors a second timeperiod into the future; and calculating a portfolio risk value based onthe adjusted holding amount and the one or more risk factors simulated asecond time period into the future.